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Results of an experimental study of the behavior of St.3, 20Kh13, and 08Kh18N10T steels under static and dynamic loading are reported. The influence of the strain rate and temperature on characteristics of strength and plasticity is studied. Based on the data obtained, the parameters of the Johnson-Cook model are determined. This model is used in commercial software to describe the yield surface radius as a function of loading parameters. The adequacy of the identified model is verified in a series of special test experiments.

This paper considers a homogeneous isotropic elastic body bounded by concentric spheres and acted upon by axisymmetric unsteady volume forces. Displacement fields are determined using series expansions in Legendre and Gegenbauer polynomials, Laplace transforms in time, and integral representations with kernels in the form of Green's functions. Explicit formulas for the Green's functions are constructed that allow accurate determination of the originals. Examples of the calculations are presented.

A mathematical model is developed within the framework of equations of damaged medium mechanics to describe the processes of viscoplastic straining and damage accumulation in structural steels with allowance for fatigue and creep of the material. A model of damage summation due to interaction of low-cycle fatigue and creep of the material is proposed. Material parameters and scalar functions of equations of mechanics of damaged media are determined. Viscoplastic straining and fatigue-induced damage accumulation in 08Kh18N10T and 12Kh18N9 are studied numerically, and the data obtained are compared with available results of physical experiments.

The distribution of the energy of a piezoelectric actuator between normal modes (Lamb waves) as a function of the source parameters and frequency is studied by solving the dynamic contact problem of the interaction between a flexible piezoelectric patch and a flexible elastic substrate with explicit representations for the excited traveling waves. Zones of the maximum and minimum energy of the fundamental modes are determined in the “oscillation frequency-piezoelectric patch width” plane.

A two-dimensional model of an anisotropic crystalline material with cubic symmetry is considered. This model consists of a square lattice of round rigid particles, each possessing two translational and one rotational degree of freedom. Differential equations that describe propagation of elastic and rotational waves in such a medium are derived. A relationship between three groups of parameters is found: second-order elastic constants, acoustic wave velocities, and microstructure parameters. Values of the microstructure parameters of the considered anisotropic material at which its Poisson's ratios become negative are found.

A locally equilibrium model of mechanodiffusion which comprises a coupled system of motion equations for an elastic body and a mass transfer equation is used to solve the two-dimensional nonstationary problem of elastic diffusion for an isotropic one-component layer. The solution is constructed using Fourier series, Laplace time transforms, and Fourier transforms for the spatial coordinate. The Laplace transform originals are found analytically, and the Fourier transforms are inverted by quadrature formulas.

This paper describes the results of experimental studies on penetration of cylindrical projectiles into concrete and reinforced concrete at impact velocities reaching 0.5 km/s. An algorithm is proposed for calculating the depth of penetration of a projectile, making it possible to find the depth of penetration of high-strength steel projectiles with a mass of up to 13.5 kg into concrete on the basis of measurements of the specific work required to remove concrete using projectiles with a mass of up to 8 g.

This paper describes the dependence of the solution of the problem of equilibrium of a Timoshenko plate and the total energy functional of the plate on the surface perturbation, which is an oblique crack. The nonlinearity of the problem is caused by the boundary conditions in the form of inequalities (conditions such as the Signorini conditions), which simulate mutual nonpenetration of the opposite crack faces. The continuous dependence of the solution of the problem on the perturbation of the crack length is established. A formula for the energy functional derivative of the perturbation of the crack length is obtained.

Homogeneous and two-layer half-spaces consisting of an anisotropic elastic, isotropic viscoelastic, or poroelastic material are considered. The Kelvin-Voigt model and the model with the Abel kernel are used as models of the viscoelastic material; the poroelastic material is studied within the framework of the model of the compressible Biot material. The case where the half-space contains a cavity is also considered. Propagation of surface waves is studied by the boundary element method. The numerical solution involves the method of collocations for a regularized boundary integral equation.

A model taking into account finite deformations is constructed for the behavior of a shape memory polymer which undergoes a transition from the highly elastic to the vitreous state and back during deformation and temperature change. The obtained relations are tested on problems which have experimental support.